Query_1

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course Phy 231

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ph1 query 1

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Question: `qExplain in your own words how the standard deviation of a set of numbers is calculated.

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Your solution:

The Standard Deviation is calculated by:

First calculating the Average Squared Deviation as follows:

1) Squaring the deviations

2) Averaging them then dividing by one less of the total

3) taking the square root of this result.

Second Take the square root of the Average Squared Deviation:

Standard Deviation = (Average Squared Deviation) ^ (1/2)

confidence rating #$&*: 3

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Question: State the given definition of the average rate of change of A with respect to B.

Briefly state what you think velocity is and how you think it is an example of a rate of change.

In reference to the definition of average rate of change, if you were to apply that definition to get an average velocity,

what would you use for the A quantity and what would you use for the B quantity?

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Your solution:

Average rate of change of A with respect to B is:

Average rate of change of A with respect to B = 'delta A / 'delta B.

Velocity is the change in position with repect to time:

Velocity = 'delta position / delta time.

average rate = 'delta A / 'delta B

confidence rating #$&*: 3

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Given Solution:

A rate is a change in something divided by a change in something else.

This question concerns velocity, which is the rate of change of position: change in position divided by change in clock

time. **

NOTE ON NOTATION

Students often quote a formula like v = d / t. It's best to avoid this formula completely.

The average velocity on an interval is defined as the average rate of change of position with respect to clock time. By

the definition of average rate, then, the average velocity on the interval is v_ave = (change in position / change in clock

time).

One reason we might not want to use v = d / t: The symbol d doesn't look like a change in anything, nor does the symbol t.

Also it's very to read 'd' and 'distance' rather than 'displacement'.

Another reason: The symbol v doesn't distinguish between initial velocity, final velocity, average velocity, change in

velocity and instantaneous velocity, all of which are important concepts that need to be associated with distinct symbols.

In this course we use `d to stand for the capital Greek symbol Delta, which universally indicates the change in a quantity.

If we use d for distance, then the 'change in distance' would be denoted `dd. It's potentially confusing to have two

different d's, with two different meanings, in the same expression.

We generally use s or x to stand for position, so `ds or `dx would stand for change in position. Change in clock time

would be `dt. Thus

v_Ave = `ds / `dt

(or alternatively, if we use x for position, v_Ave = `dx / `dt).

With this notation we can tell that we are dividing change in position by change in clock time.

For University Physics students (calculus-based note):

If x is the position then velocity is dx/dt, the derivative of position with respect to clock time. This is the limiting

value of the rate of change of position with respect to clock time. You need to think in these terms.

v stands for instantaneous velocity. v_Ave stands for the average velocity on an interval.

If you used d for position then you would have the formula v = dd / dt. The dd in the numerator doesn't make a lot of

sense; one d indicates the infinitesimal change in the other d.

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Self-critique (if necessary):

v_ave = 'ds / 'dt = change in position / change in time.

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Self-critique rating: 3

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Question: Given average speed and time interval how do you find distance moved?

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Your solution:

I would use Algebra as follows:

V_ave = 'ds / 'dt

'ds = v_ave * 'dt

distance = average velocity * change in time.

confidence rating #$&*: 3

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Given Solution:

** You multiply average speed * time interval to find distance moved.

For example, 50 miles / hour * 3 hours = 150 miles. **

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Self-critique (if necessary):

ok

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Self-critique rating: 3

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Question: Given average speed and distance moved how do you find the corresponding time interval?

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Your solution:

I would use Algebra:

v_ave = 'ds / 'dt

'dt = 'ds / v_ave

Change in time = change in position / average velocity

confidence rating #$&*: 3

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Given Solution:

** time interval = distance / average speed. For example if we travel 100 miles at 50 mph it takes 2 hours--we divide the

distance by the speed.

In symbols, if `ds = vAve * `dt then `dt = `ds/vAve.

Also note that (cm/s ) / s = cm/s^2, not sec, whereas cm / (cm/s) = cm * s / cm = s, as appropriate in a calculation of

`dt. **

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Self-critique (if necessary):

ok

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Self-critique rating: 3

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Question: Given time interval and distance moved how do you get average speed?

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Your solution:

v_ave = 'ds / 'dt

average speed = change in position / change in time

confidence rating #$&*: 3

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Given Solution:

** Average speed = distance / change in clock time. This is the definition of average speed.

For example if we travel 300 miles in 5 hours we have been traveling at an average speed of 300 miles / 5 hours = 60 miles

/ hour. **

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Self-critique (if necessary):

ok

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Self-critique rating:

#$&*

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Question: Given time interval and distance moved how do you get average speed?

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Your solution:

v_ave = 'ds / 'dt

average speed = change in position / change in time

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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Given Solution:

** Average speed = distance / change in clock time. This is the definition of average speed.

For example if we travel 300 miles in 5 hours we have been traveling at an average speed of 300 miles / 5 hours = 60 miles

/ hour. **

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Self-critique (if necessary):

ok

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Self-critique rating:

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